ABSTRACT
Children come to school with a rich and varied set of informal experiences of space. Looking at shape and form in the world, children build intuitions about perspective, symmetry, and similarity. Walking in their neighborhoods, children reason about distance, direction, and their composition (e.g., routes). Drawing what they see, children represent and use elements of space for play and for communication. Building structures with blocks, toothpicks, or Tinkertoys, children experience firsthand how shape and form play roles in function (e.g., round objects roll; most others do not) and structure (e.g., some structures bear loads; others do not). Everyday experiences like these, and the informal knowledge children develop over time by participating in them, constitute a springboard for developing children’s mathematical understanding of space: a children’s geometry. For example, senses of position and direction derived from walking can be elaborated mathematically in a variety of ways—as coordinate systems, as compass directions, as maps, and as dynamic Logo models. 1 Each of these mathematical forms of thought has antecedents in children’s experiences as well (e.g., coordinate systems in city blocks, maps in children’s drawings), and, collectively, these experiences constitute a good grounding for making mathematical sense of the spatial world.
